Analyzing the primary root branching pattern

In order to explore whether lateral root type repartition along the primary root was random or somehow structured, we analyzed the distribution of lateral root types (A, B and C) along the primary root. We first evaluated the impact of the root type on the length of the interval between a lateral root and its nearest neighbor in the rootward direction (Baskin et al., 2010). No difference was found between the mean interval length for the three root types in both species (ANOVA, p-value = 0.83 and 0.7 for pearl millet and maize respectively) (Table II-

1). The same type of analysis was conducted separating intervals into 9 groups, depending on

the types of the two lateral roots delimiting the interval (Supplementary Table II-5). No effect of the lateral root types was found on the interval lengths (ANOVA, p-value = 0.52 and 0.39 for pearl millet and maize respectively). Hence, our results indicate that there is no influence of root types on interval lengths between two successive lateral roots.

Table II-1 Length of the interval between successive lateral roots, classified according to the lateral

root delimiting the interval in the shootward direction. No significant differences between the means were found (ANOVA, p = 0.83 and p = 0.70 for pearl millet and maize respectively).

Lateral root type in the shootward direction A B C Pearl millet Maize Pearl millet Maize Pearl millet Maize Sample size 165 237 296 814 785 1950 Mean (cm) 0.22 0.16 0.21 0.16 0.21 0.17 Standard deviation (cm) 0.27 0.16 0.27 0.15 0.19 0.15

We then questioned whether lateral root type sequences were random or somehow structured. We first computed the Spearman rank autocorrelation function for these sequences. The autocorrelation function for positive lags was within the confidence interval corresponding to the randomness assumption for most of the plants, indicating that the distribution of the different lateral root types along the primary root was stationary and

suggesting no marked dependencies between successive lateral root types. This finding was consistent with the growth rate profile length frequency distributions being similar for the three types (Supplementary Table II-4). Since growth rate profile lengths directly depend on the emergence time of each lateral root and are thus related to the lateral root position on the primary root, this suggests that the proportions of the 3 types along the primary root were essentially stationary. We further analyzed primary root branching sequences applying a statistical modeling approach. To this end, we modeled potential dependencies between successive lateral root types described from the collar to the root tip. Three-state variable- order Markov chains, each state corresponding to a lateral root type, were built. The memories of variable-order Markov chains were selected (Csiszár and Talata, 2006) for each primary root branching sequence and for samples of branching sequences corresponding to each species. For all plants and for both species, a zero-order Markov chain was selected. This confirmed that the type of a lateral root was independent of the type of the previous lateral roots. Hence, our results indicate that there is no influence of the lateral root growth pattern on the distance to or on the growth pattern of the next lateral root.

We checked whether the length of the interval between successive lateral roots and the lateral root type proportions varied or not among individual plants. The mean interval lengths were not equal in all plants (ANOVA, p < 10-5 for pearl millet and p < 10-6 for maize). Plants were thus classified according to Tukey’s Honest Significant Difference. Two overlapping groups were found, both for pearl millet and maize (Figure II-8), with average interval length ranging from 0.31 to 0.21 cm in pearl millet, and from 0.25 to 0.14 cm in maize.

Significant differences among plants were also found for lateral root type proportions both for pearl millet and maize (Kruskal-Wallis test, p < 10-10 and p < 10-15 respectively, Figure II-

9). For pearl millet, the 8 plants were separated into 3 significantly different groups with two

overlapping. The proportion of type A roots ranged from 0.06 to 0.21 between these groups. The 13 maize plants were separated into 6 groups, with some overlaps between groups, type A root proportion ranging from 0 to 0.2. These results indicated that both species show significant inter-individual differences in terms of interval lengths and lateral root type proportions. However, and despite individual differences between plants in terms of lateral root type proportions, the stationary random branching pattern was markedly conserved in all plants. As all plants among species are supposed to be genetically homogeneous, we hypothesize that small environmental variations, either during the grain filling and maturation period or during the experiment itself, could explain differences in lateral root type proportions. The link between interval length and lateral root type proportions in each plant is explored in Supplementary Result II-1.

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Figure II-8 Distribution of interval lengths between successive lateral roots for each plant in pearl

millet (A) and maize (B) species and plant group assignation according to Tukey’s Honest Significant Difference test. Outliers above 1 cm were curtailed. Numbers along the x – axis refer to plant ID.

Figure II-9 Proportion of root types for each plant in pearl millet (A) and maize (B) species and plant

group assignation according to Kruskal-Wallis test. Tile areas are proportional to the number of roots in each category. Total lateral root number per plant ranged from 119 to 248 for pearl millet and from 82 to 352 for maize and are proportional to tile width. Numbers above tiles refer to plant ID.

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